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If y= tan^(-1)sqrt((1-sinx)/(1+sinx)), t...

If y= `tan^(-1)sqrt((1-sinx)/(1+sinx))`, then the value of `(dy)/(dx)` at x= `(pi)/6` is.

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`y = tan^(-1) sqrt((1-sin x)/(1+sin x))`
`= tan^(-1) sqrt(1-cos ((pi/2)-x)/(1+cos ((pi/2)-x))`
`= tan^(-1) sqrt(2 sin^2((pi/4)-(x/2))/2 cos^2(pi/4)-(x/2))`
`= tan^(-1) tan ((pi/4)-(x/2))`
`= (pi/4)-(x/2)` ...
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